Intermittent problems are evil...but a great challenge!
Had the same frustrating problem a long time ago with a Mini Marcos. Very often in cold mornings it failed so I ended up always parking it pointing down hill just in case...and also became very generous in offering a colleague (living in the same house) a ride to work. But going home from work in the afternoons it always started on the first turn. Just like you I checked and double checked everything (think I even changed the solenoid and starter) but with no change in behaviour
With the battery in the boot I later learned that the loss of "starting power" with a three and a half meter plus cable could be pretty big. So I changed the cable to a new one with larger diamter and also a new quality battery and then never experienced any problems again.
It could be multiple reasons...just check the system carefully again and you will solve it! Good luck
